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Class 


The  Relationship  Existing  between 

the  Weight  of  a  Falling  Drop 

and  the  Diameter  of  the 

Tip  from  which 

it  Falls 


DISSERTATION 


SUBMITTED  IN  PARTIAL  FULFILMENT  OF  THE   REQUIRE- 
MENTS FOR  THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY 
IN  THE  FACULTY  OF  PURE  SCIENCE  IN  COLUMBIA 
UNIVERSITY  IN  THE  CITY  OF  NEW  YORK. 


BY 


JESSIE  YEREANCE  CANN,  A.B.,  A.M. 

NEW  YORK  CITY 
1911 


EASTON,  PA.: 

ESCHBNBACH  PRINTING  COMPANY. 
1911. 


The  Relationship  Existing  between 

the  Weight  of  a  Falling  Drop 

and  the  Diameter  of  the 

Tip  from  which 

it  Falls 


DISSERTATION 


SUBMITTED  IN  PARTIAL  FULFILMENT   OF  THE    REQUIRE- 
MENTS FOR  THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY 
IN  THE  FACULTY  OF  PURE  SCIENCE  IN  COLUMBIA 
UNIVERSITY  IN  THE  CITY  OF  NEW  YORK. 


BY 


JESSIE  YEREANCE  CANN,  A.B.,  A.M. 

NEW  YORK  CITY 
1911 


EASTON,  PA.  : 

ESCHENBACH  PRINTING  COMPANY. 
1911. 


ACKNOWLEDGMENT. 

The  following  investigation  was  suggested  by  and  carried 
out  under  the  direction  of  Professor  J.  Livingston  R.  Morgan. 
The  author  desires  to  extend  her  sincere  thanks  and  ap- 
preciation to  Professor  Morgan  for  his  helpful  assistance, 
advice  and  encouragement  during  the  course  of  the  work. 

J.  Y.  C. 


226928 


The  Relationship  Existing  between  the  Weight  of 

a  Falling  Drop  and  the  Diameter  of  the  Tip 

from  which  it  Falls 

INTRODUCTION. 
Object  of  the  Investigation. 

In  1864,  Thomas  Tate,1  as  the  result  of  his  experiments 
with  water,  announced  the  following  laws : 

I.  Other  things  being  the  same,  the  weight  of  a  drop  of 
liquid  (falling  from  a  tube)  is  proportional  to  the  diameter 
of  the  tube  in  which  it  is  formed. 

II.  The  weight  of  the  drop  is  in  proportion  to  the  weight 
which  would  be  raised  in  a  tube  with  a  bore  equal  to  the 
outer  diameter  by  capillary  action. 

III.  The  weight  of  a  drop  of  liquid,  other  things  being  the 
same,  is  diminished  by  an  augmentation  of  temperature. 

Tate's  experiments  were  all  made  with  thin- walled  glass 
tubing,  varying  in  diameter  from  0.1-0.7  of  an  inch,  the 
orifice  in  each  case  being  ground  to  a  ''sharp  edge,  so'  that 
the  tube  at  the  part  in  contact  with  the  liquid  might  be  re- 
garded as  indefinitely  thin."  His  weights  were  calculated 
from  the  weight  of  from  five  to  ten  drops  of  liquid,  which 
formed  at  intervals  of  forty  seconds,  and  were  collected  in  a 
weighed  beaker. 

Tate's  law  is  generally  accepted  as  equivalent  to  the  ex- 
pression 

w  =  2  it  r  T, 

where  w  is  the  weight  of  the  falling  drop,  r  the  radius  of  the 
tube  on  which  it  forms,  and  j-  is  the  surface  tension  of  the 
liquid.  This  expression  is  not  exactly  as  Tate  intended  it 
to  be  formulated,  for  his  law  simply  states  a  proportionality; 
so  that  the  expression  should  be 

w  =  2  n  r  f  K, 

where  K  is  some  constant  which  will  transform  the  pro- 
portionality into  an  equality. 

1  Phil.  Mag.,  4th  Ser.,  27,  176  (1864). 


It  has  also  been  shown  by  Morgan  and  Stevenson,1  Morgan 
and  Higgins2  and  Morgan  and  Thomssen3  contrary  to  the 
conclusions  of  all  other  workers  since  Tate  that  the  weight  of 
a  single  drop  of  a  non-associated  liquid  falling  from  a  definite 
tip  is  regulated  by  the  following  laws: 

I.  The  quantity  w( — J  (w  =  weight  of  drop  in  milli- 
grams, M  =  molecular  weight,  d  =  density)  is  a  linear  func- 
tion of  the  temperature,  becoming  zero  at  a  point  6°  below 
the  observed  critical  temperature  or  a  fictitious  critical 
» temperature.  Expressed  mathematically  we  have  then  (in 
the  form  of  Ramsay  and  Shields,  for  surface  tension) 


w 


where  tc  is  the  critical  temperature  (observed  or  fictitious) 
and  t  is  the  temperature  of  observation  and  k  a  universal 
constant,  defined  by  the  equation 

MX  §        /M 


although,  as  has  been  shown  by  Morgan,3  it  should  not  be 
calculated  in  this  way,  owing  to  the  multiplication  of  error, 

but  from  w( — j     =  £3(288.5 — t  —  6)  for  benzene  once  for  all. 

II.  The  temperature  coefficient  of  the  function  w(—  J 

i.  e.y  the  kB  of  the  above  equation  is  a  universal  constant  for 
such  liquids,  leading,  as  has  been  shown  by  Morgan,3  to  the 
same  value  of  tc  for  any  one  non-associated  liquid  at  all 
temperatures  of  observation. 

It  has  further  been  shown  by  Morgan  that  the  above  laws 
hold  also  when  applied  to  the  results  of  Ramsay  and  Shields 
of  surface  tension,  thus  confirming  Tate's  second  law. 

1  /.  A.  C.  S.,  30,  360-376  (1908). 

2  Ibid.,  30,  1055-68  (1908). 

3  Ibid.,  May,  1911. 


The  object  of  this  investigation  was  to  establish  con- 
clusively the  truth  of  the  first  of  the  above  laws,  i.  e.,  to  make 
an  exhaustive  study  of  the  relationship  existing  between  the 
weight  of  a  falling  drop  and  the  diameter  of  the  tip  from 
which  it  falls.  For  this  purpose  sixteen  different  tips  were 
employed,  varying  in  size  from  about  3  mm.  to  approximately 
8  mm.  in  diameter.  Five  representative  liquids,  including 
that  with  practically  the  largest,  as  well  as  that  with  the 
smallest  possible  drop  volume,  were  chosen  and  the  relation- 
ship between  the  drop  weights,  and  the  different  sized  tips 
studied  exhaustively. 

Apparatus  and  Method, 

The  apparatus  used  in  this  work  is  a  new  and  simple  form 
designed  by  Morgan1  and  especially  adapted  to  the  general 
needs  of  the  investigator  in  other  lines  of  chemistry.  By 
it  the  weight  of  a  falling  drop  of  any  liquid  from  any  desired 
tip  can  be  found  at  various  temperatures,  up  to  within  a  few 
degrees  of  the  boiling  point,  with  very  great  accuracy,  every 
possible  form  of  variable  error  having  been  foreseen  and 
avoided.  As  the  results  of  this  work  show,  the  method 
is  indeed  one  of  very  great  accuracy. 

In  order  to  exclude  any  variation  in  the  results  due  to 
changing  temperature,  all  measurements  were  made  in  a 
constant  temperature  bath.  This  was  of  the  Ostwald  gas 
type  with  a  transparent  bath,  stirred  by  a  small  electric 
motor.  The  temperature  employed  was  27.8°  C.,  the  greatest 
variation  recorded  being  ±0.03°.  The  thermometer  used 
here  was  a  certified  one  reading  in  fiftieths  of  a  degree. 

The  five  representative  non-associated  liquids  were 
quinoline,  pyridine,  benzene,  ether  and  carbon  tetrachloride . 
These  five  liquids  were  considered  the  best  because  of  their 
great  differences  in  density,  surface  tension  and  general 
physical  properties  (i.  e.,  viscosity,  etc.). 

The  weight  of  the  drop  was  obtained  by  finding,  first, 
that  of  thirty  or  more  drops,  in  the  following  manner.  The 
liquid  is  sucked  over  from  the  supply  vessel  into  the  capillary 

1 /.  A.  C.  S.,  March,  1911. 


8 

tubing,  and  allowed  to  form  a  drop  on  the  tip.  This  drop  is 
held  at  as  nearly  as  possible  its  maximum  size  for  5  minutes, 
so  that  the  vessel  may  become  saturated  with  the  vapor  of 
the  liquid  used.  Next,  thirty  consecutive  drops  are  allowed 
to  fall  each  drop  falling  of  its  own  weight  alone,  and  the  time 
of  the  entire  determination  noted.  Then  the  vessel  with  the 
vapor  and  thirty  drops  is  weighed,  being  wiped  with  cheese- 
cloth to  constant  weight.  After  the  apparatus  has  been  set 
up  again,  and  has  assumed  the  temperature  of  the  bath  by 
remaining  in  it  for  a  half  hour  or  more,  another  determina- 
tion, a  "blank"  is  taken.  This  time  the  liquid  is  sucked  over 
in  the  same  manner  as  before,  the  drop  being  allowed  to 
hang  five  minutes,  but  only  five  consecutive  drops  are  al- 
lowed to  fall,  the  sixth  drop  being  held  on  the  tip  without 
falling  for  the  balance  of  the  time  consumed  by  the  first 
determination.  In  this  way  the  liquid  in  the  weighing 
vessel  in  each  determination  is  exposed  for  the  same  length 
of  time  to  the  same  evaporating  influence  both  for  the  hang- 
ing drop  and  the  liquid  which  has  fallen,  so  that  the  total 
loss  is  the  same  in  both  cases.  By  subtracting  this  5 -drop 
blank  from  the  3O-drop  determination,  the  weight  of  one 
drop  is  obtained,  after  dividing  the  difference  by  25.  Exactly 
the  same  method  is  to  be  employed  with  each  liquid  used. 

The  densities  used  were  those  determined  by  Morgan  and 
Higgins. 

Liquids. 

The  benzene  used  in  this  work  was  Kahlbaum's  special  K. 
The  quinoline  was  distilled  frequently,  for  when  it  contains 
water  the  results  are  too  low,  while  when  allowed  to  stand 
it  decomposes,  becoming  thicker  and  yellow,  and  giving  high 
results.  Because  of  the  "sticky"  nature  of  quinoline  great 
care  had  to  be  taken  each  time  between  determinations  to 
clean  the  capillary  tube  very  thoroughly,  and  then  to  prevent 
liquid  rising  until  the  first  drop  was  run  over,  so  that  no 
threads  of  liquid  would  be  spurted  over  before  the  drop, 
and  thus  cause  the  weight  to  be  too  large.  The  pyridine 
used  was  Kahlbaum's  special  K,  and  remained  unchanged — 
pure  and  colorless — throughout  the  entire  period  of  work. 


It  was  found  in  working  with  pyridine,  particularly  with  the 
larger  tips,  that  each  drop  had  to  be  drawn  back  into  the 
capillary  tube,  before  being  allowed  to  fall,  so  that  each 
drop  would  be  exactly  like  the  first  drop.  It  was  apparent 
to  the  eye  in  these  cases  that  the  regular  procedure  caused 
the  successive  drops  to  grow  smaller,  and  that  the  liquid  did 
not  extend  out  to  the  edge  of  the  tip,  and  hence  would  give 
too  low  a  result.  The  carbon  tetrachloride  used  was  from 
Baker  and  was  redistilled  often.  Great  care  had  to  be 
taken  in  making  determinations  with  this  liquid,  for  the  drop 
volume  and  surface  tension  are  so  small  that  unless  the  drop 
is  perfectly  controlled  at  the  moment  of  fall  the  result  will 
be  too  large.  With  tips  larger  than  4.5  mm.  this  control  is 
extremely  difficult,  if  possible  at  all  on  this  form  of  apparatus, 
and  the  results  obtained  are  always  too  high.  This  perfect 
control,  however,  is  one  of  the  essential  principles  of  the  drop 
weight  method.  The  ether  was  from  Kahlbaum,  and  was  al- 
ways redistilled  several  times  before  a  determination.  With- 
out redistillation  the  results  are  always  found  to  be  too 
high. 

Results. 

In  Tables  I-V  are  the  experimental  results  obtained  with 
the  sixteen  tips  used  for  the  liquids  studied,  together  with  the 

/M\  § 
values  of  the  function  w  (  —  I  ,  where  w  is  the  drop  weight  and 

d  the  density,  both  at  the  same  temperature,  while  M  is  the 
molecular  weight. 

TABLE  I. — BENZENE. 


wt. 

Diameter     30  drops 
of  tip.      and  vessel. 
Mm.          Grams. 

AT.  wt.                 Wt.             Av.  wt. 
of  30  drops         5  drops        of  5  drops 
and  vessel,     and  vessel,    and  vessel. 
Grams.            Grams.          Grams. 

Av.  wt.  of 
i  drop.        a/f^S 
Mgs.             vrf/   ' 

10.3560 

9.9222 

3.048 

I0.356I 

10.35606       9.9222       9.9222 

17-355    347-51 

I0.356I 

3-929 


11.1960        10.6569 

11.1960  11.1960  10.6569  10.6569  21.564431.77 

II . 1960 


10 


TABLE  I. — (Continued}. 
[10.4067  9-8585 

4.  ooo  I0'4°67 

jio.4071  10.40695  9/8587  9.8586  21.934439.18 

[10.4073 


4-5I4 


i 


10.0359 


9.4292 


I0-0359  10.03586  9-429!  9  42915  24.269  485.72 
10.0358 

9.9938  9.3626 

9.9938  9.3626 

9-9936  9-99373  9-3626  9.3626  25.245  505.47 

9-9937 


4.978 


10.8887         10.2198 

10.8887  10.88863  10.2198  10.2198  26.753  535-67 

10.8885 


5-306 


(25  drops) 
11.2625 
ii .2622 


10.6918 


11.2619  11-26233  10.6918  10.6918  28.526  571.17 
ii .2627 


11.2137  10.4754 

soil  Jo-4756 

,11.2137  11-2137  10.4755  10.4755  29.528  591-23 

[11-2137  10.4755 


5-500 


9-7253 


8-9873 


9.7255  9.7256   8.9873  8.9873  29.532  591-31 
9.7260 


5.689 


9-7554 


8.9922 


9-7555  9-7554   8.9920  8.9921  30.532  611.33 
9-7553 


5-845 


6.200 


11.3907 


10.6067 


11.3905  11.39056  10.6068  10.60683  31.349  627.70 
11.3905       10.6070 

11.3815  10.7159 

11.3816  11.38163  10.7159  10.7159  33.287  666.48 
11.3818 


II 


6-550 


6.844 


7-387 


TABLE  I. — (Continued). 
25  drops) 

11-5351  10.8287 

n-5357 

n-5357  10.8282 

n-5357 

11.5352   11.53548   10.8285   10.82846  35-351   707-82 
H-5357 
n-5357 
H-535I 

(25  drops) 

10.4305         9.6872 

10.4302 

10.4299  10.43023     9.6870     9.6871     37-156  743-97 

10.4303 
(25  drops) 

11.4210  10.6057 

11.4207  11.42073  10.6058   10.60575   10.749  815.91 

ii .4205 


(25  drops) 

.   (11.4978  10.6215 

7.859)11.4980  11.4981     10.6215   10.6215     43.83 
[11.4985 

TABLE  II. — QUINOLINE. 


877.58 


Wt.  Av.  wt. 

Diameter      30  drops     of  30  drops 
of  tip.       and  vessel,  and  vessel. 
Mm.          Grams.         Grains. 


3.048 


4-000 


4-5I4 


10.6755 

10.6759  10.67566 

10.6756 

10.8235 

10.8238  10.82376 

10.8240 

10. 802  I 

IO.8O2O  IO.8O2 I 
10.8022 

(20  drops) 
10.0749 
10.0749 

10.0755  10.0752 
10.0755 


Wt.  Av.  wt. 

5  drops        of  5  drops  Av.  wt.  of 

and  vessel,  and  vessel.  i  drop 

Grams.          Grams.  Mg. 

9  9739 
9-9743 
9-9741 


9-9594 
9-9595 


'(f)1- 
9.9741  28.063  677.48 

9-95945  34-573  834.62 
848.93 


9.9229 

9.9230  9.92296  35-165 

9.9230 


9-4979 

9.4979     9-4979     38-487  929-11 


12 


4-978 


5-5oi 


TABLE 
(20  drops) 
ii .4198 

11.4196  11.4197 
11.4197 

11.7336 

11.7330  11-7333 
n-7333 


{10.2444 

5 . 500  10 . 2443  10 . 2444 
[10.2445 


5.689 


10.2932 
10.2939 


10.2938  10.2935 
10.2931 

[11.6891 

5.845) 11.6892  11.68923 
[ i i . 6894 


(20  drops) 

1 i . 6005 

i i. 6010  11.6007 

1 i . 6006 

(20  drops) 
11.7617 
ii .7611 

11.7617  11.76158 
11.7618 


II. — (Continued'). 

10.7825 
10.7825  10.7825 


10.5604 
10.5604  10.5604 


9.0713 

9.0715  9-0714 

9.0714 

9 . 0802 

9 . 0798  9 . 0800 

10.6955 
10.6953  10.6954 


6.200 


6-550 


(25  drops) 
[ 10.6615 

6.844! 10.6605  10.66106 
10.6612 


(20  drops) 

11 .6620 
11.6615  11.66186 

11 .6621 

(20  drops) 
11.7521 
11.7517  11.75176 


7-859 


10.8104 
10.8106  10.8105 


10.9261 
10.9261  10.9261 


9.7894 

9.7894  9-7894 


10.7150 
10.7150  10.7150 


10.7372 
10.7372  10.7372 


42.48  1025.52 
46.916  1132.61 
46.92  1132.71 

48.54  1171.00 
49.692  1199.61 

52.68  1271.73 

55.698  1344-62 
58.111  1402.87 
63.124  1523-90 
67.638  1632.10 


13 
TABLE  III. — PYRIDINE. 

Wt.               Av.  wt.  Wt.              Av.  Wt. 

Diameter      30  drops     of  30  drops  5  drops  of  5  drops  Av.  wt.  of 

of  tip.       and  vessel,  and  vessel.  and  vessel,  and  vessel.  i  drop 

Mm.           Grams.          Grams.  Grams.           Grams.  Mg. 


3.048 


io.  5  H4  9-9470 

lo. 5 H3  10.51446     9  9470     9-947O     22.699     425-42 

10.5147 


[10.6369  9.9288 

3 . 929  10 . 6368  10 . 6369   9-9287  9 . 9288  28 . 324  530 . 85 
[10.6370         9.9289 

[ 10. 7625         10.0422 

4.ooolio.7628  10.76246  10.0422  10.0422  28.81   539-96 
[10.7621 

10.2604          9.4654 


4-5I4 


4.978 


5-5QI 


10.2610  10.2606  9.4651  9  46533  31.811  596.20 

10.2604  9-4655 

ii . 1390  10.2609 

11.1392  11.13913  10.2605  10.2607  35-137  658.54 

11.1392 

11.1435  10.1744 

11.1436  11.1435  10.1745  10.17445  38.762  726.48 
11.1434 


[10.0003         9-0311 

5.500110.000410.00033  9.0312  9.0311638.767  726.57 
10 . 0003         9 • 03 i 2 


5.689 


5.845 


10.0387  9-0363 

10.0385  10.0384  9.0368  9-03655  40.074  751-07 

10.0380 

11.6846  10.6545 

11.6840  11.68446  10.6546  10.65455  41.197  772.11 

I I . 6848 


(25  drops) 

[11.8020         10.8792 
I  11.8029 

'55  ] i i. 8022  11.80227  10.8795  10.87935  46.146  864.88 
ii .8020 


9-7405 
9 • 7405 


9.7405    48.20,   903-37 


TABLE  III. — (Continued). 
(25  drops) 
10.7045 

6.844    10.7044  10.7045 
10. 7046 

(25  drops)     , 
f i i . 7069 

7.387111.7069  11.7069 
[  1 1 . 7069 

(25  drops) 

f i i. 8022         10.6807 
7.859] ii .8023  11.80223  10.6806  10.68066  56.078  1051.02 


10.6599 
10.6599  10.6599 


52.35     981.15 


ii .8022 


10.6807 


TABLE  IV. — CARBON  TETRACHLORIDE. 


Wt.  Av.  wt. 

Diameter  30  drops  of  30  drops 
of  tip.  and  vessel,  and  vessel. 
Mm.  Grams.  Grams. 


Wt.  Av.  wt. 

5  drops       of  5  drops  Av.  wt.  of 

and  vessel,  and  vessel.  i  drop. 

Grams.           Grams.  Mg. 


(50  drops) 

10.5284 


10.5280 


10.5283 


10.5279 


[10.3811 

3.929!  10.3812  10.3811 
[  10.3810 


(10  drops) 

9.9077 
9.9077 


9.8895 
9.8896 

9 . 8894 


4.000 


4-514 


(50  drops) 
[  8.5932 
1  8.5937 

8.5930 

8-5931 

(50  drops) 
8.1205 
8.1208 

8.1203  8 

1 . i 204 


(10  drops) 
7 • 7934 
•59323  7-7932 


1205 


7 • 9593 
7 • 9593 
7-9594 
7 • 9593 


7 • 95933 


7. 1108 
7. 1108 


7-37I3 
7-37io 
7.3710 
7-3708 
7-37i8 


9-9077  I5-5I5  328.97 


9.8895  19.664  416.94 


7-7933  I9-998  424-03 


7.1108  22.438  475-76 


7.37118  23.526  498.83 


4.978 


TABLE  IV. — (Continued). 
r  9-5975          8.9709 
9-5977          8.9710 

9-598o  9-59775  8.9714  8.9711  25.066  531.46 
9-5978 


r ii. 3661         10.6910 
'3  '[11.3661  11.3661  10.6910  10.6910 


5-5oi 


10.8320 


10. 1265 


10.8322  10.8321  10.1265  10.1265 
10.8321 


_nn,  9-6945         8.9873 
5'5   I  9-6944  9-69445  8.9871  8.9872 

5.689  9-7327  9-7327   8.9938  8.9938 


27.004 

28.224 
28  .29 

29-556 


572.58 

598.45 
599.82 

626.69 


5.845 


11.3760 


10.6089 


11.3762  11.3761  10.6084  10.60865  30.698  650.90 


11.3761 

6.200  11.5330  11.5330  10.7172  10.7172 

6.550  11.6985  11.6985  10.8317  10.8317 

6.844  10.  6061  10.  6061  9.6906  9.6906 


TABLE  V. — ETHER. 


Wt.  Av.  wt. 

Diameter    30  drops      of  30  drops 
of  tip.     and  vessel,  and  vessel. 
Mm.         Grams.         Grams. 


Wt.  Av.  wt. 

5  drops       of  5  drops. 

and  vessel,  and  vessel. 

Grams.         Grams. 


(50  drops) 


(10  drops) 
7.2107 
7.6045  7-6045   7.2109  7.2108 


8.7205         8.4134 
3.929]  8.7206  8.7205   8.4133  8.4134 
[  8.7204         8.4135 


32-632 
34.672 
36.62 


Av.  wt.  of 

i  drop. 

Mg. 


9.843 
12.284 


691  .91 

735-17 
776.47 


219.23 
273.61 


4.000 


(50  drops)       (i i  drops) 
8.2272         7-7400 
8.2272 
8.2279  8.22743  7-7401  7-74003  12.497  278.36 


8.2274 


7.7400 


i6 

V.—  ( Continued} . 
(50  drops)  (10  drops) 

9.1339  8.5816 

A    SlJ     9-1344  8.5818 

9.1347  9.13448  8.5820  8.58194  13.813  307.67 
9-1349       8.5823 
8.5820 

[  7-7829       7-4019 

4-695  7-7831  7-7830  7-4019  7-40193  15-243  339-51 
I  7-7830       7.4020 


5-501 


5-500 


5.689 


5-845 


7.6328  7.2122 

7.6327  7.6328  7.2121  7.21216  16.825  374-76 

7.6329  7.2122 

7-7575         7-3367 

7-7574  7-75746  7-3369  7-3368  16.827  374-79 

7-7575         7-3368 


7-7775         7-3400 

7.7776  7-77753  7-3400  7-3400  17-501  389-82 

7-7775 

7-7895          7-3394 

7.7894  7-7895   7-3393  7-3394  18.004  401.02 

7-7896          7-3395 


8.9719  8.4555 

6-550)  8.9720  8.97196  8.4556  8.4555  20.659  460.14 

8.9720  8.4554 


6.844 


7.387 


7-859 


8.6478  8.1043 

8.6480  8.6479   8.1045  8.1044  21.74   484.23 

8.6479  8.1044 

8.6256  8.0254 

8.6257  8.6256   8.0255  8.0254  24.008  534-75 
8.6255  8.0253 

8.4755  7-8232 

8.4759  8.47546  7-8230  7-8231  26.095  581-23 

8.4750 


17 

On  all  three  tips  below  4.514  mm.  benzene,  quinoline, 
pyridine  and  ether  showed  drop  profiles  which  were  very 
much  larger  at  the  bottom  of  the  drop  than  at  the  top  or 
than  the  diameter  of  the  tip  itself,  so  that  on  all  these  tips  we 
should  expect  the  results  to  be  non-concordant  when  various 
liquids  are  compared,  for  the  amount  of  the  bulging,  and 
consequently  of  the  weight  of  the  liquid  falling  is  here  inde- 
pendent of  the  diameter  of  the  tip  from  which  it  falls.  On 
the  tips  from  4.514  up  to  and  including  5.507  the  control  of  the 
drop  was  perfect  with  all  the  liquids  except  carbon  tetrachloride, 
and  at  most  the  profile  of  the  drop  showed  that  the  edges  of  the  lower 
part  are  simply  a  continuation  of  the  edges  of  the  tip  and  none 
extends  beyond. 

Carbon  tetrachloride  can  only  be  perfectly  controlled  on 
tip  of  4.514  and  on  the  two  sizes  below,  the  drop  on  all 
the  larger  tips  spurting  at  the  last  moment  and  carrying 
down  with  it  an  excess  of  liquid.  This  is  due  to  the  small 
drop  volume,  together  with  the  small  surface  tension  of  this 
liquid,  which  makes  the  drop  at  its  lower  extremity  very 
small,  and  very  liable  to  break  down. 

It  is  to  be  remembered  here  that  the  perfect  control  is  lost 
only  on  the  form  of  apparatus  in  question,  for  the  long 
capillary  burette  used  by  Morgan  and  Higgins  would  un- 
doubtedly show  perfect  control  on  considerably  larger  tips, 
for  the*  long  tail  of  liquid  in  the  narrow  capillary  only  allows 
a  very  slow  formation  of  the  drop  at  best. 

Bther  is  found  to  be  difficultly  controlled  on  the  5.689; 
while  only  on  the  larger  ones  is  trouble  experienced  with 
benzene,  pyridine  and  quinoline.  We  should  expect  then 
on  the  tips  from  3.929  up  to  and  including  4.514  that  carbon 
tetrachloride  would  be  the  criterion  for  other  like  liquids,  for 
its  drop  volume  is  so  small  that  the  edges  of  the  drop  never 
extend  beyond  lines  parallel  to  the  edges  of  the  tip  itself. 

As  soon  as  perfect  control  is  lost,  the  drop  which  falls  is 
too  large  for  it  does  not  fall  of  its  own  weight  alone,  but  has 
projected  with  it  some  of  the  liquid  which  under  perfect  con- 
trol would  remain  on  the  tip.  This  increase  in  weight  con- 
tinues to  increase  with  the  diameter  of  the  tip  until  the 


i8 

maximum  drop  volume  has  been  attained,  after  which  the 
edges  of  the  drop  pull  away  from  the  tip;  when,  provided 
the  control  were  still  perfect,  too  small  a  drop  for  that  tip 
would  result.  As  the  control,  however,  is  not  perfect,  we 
should  expect  the  value  to  become  too  high  as  control  is  lost, 
then  to  become  correct  when  lack  of  control  is  just  balanced 
by  the  decreasing  effect  of  the  drop  pulling  away  from  the 
tip;  and  finally  the  drop  would  probably  remain  of  the  same 
weight  on  all  larger  tips.  Although  the  diameters  of  the 
above  tips  were  measured  on  a  dividing  engine,  the  mean  of  a 
number  of  determinations  on  each  of  three  diameters  being 
taken,  the  accuracy  is  certainly  not  much  greater  than  o.oi 
mm.  owing  to  the  fact  that  the  tips  were  never  perfectly 
circular  in  section,  and  in  some  cases  flaws  had  developed 
in  the  edge  which  made  the  measurement  difficult,  although 
probably  it  affected  the  drop  weight  but  slightly.1  In 

TABLE  VI. 

Values  for-. 


Diameter 
of  tip.    Benzene. 

Quinoline. 

Pyridine. 

d 

ecu. 

Ether. 

Mm. 

Mg. 

Mg. 

Mg. 

Mg. 

Mg. 

3 

.048 

.5 

.6970 

9 

.2069 

7 

-4470 

5 

.O9O2 

3 

.2291 

3 

.929 

5 

.4884 

8 

.7992 

7 

.2089 

5 

0008 

3 

.1265 

4 

.000 

5 

.4835 

8 

•7913 

7 

.2025 

4 

9995 

3 

•1243 

4 

•  514 

5 

.3762 

8 

5260 

7 

.0471 

4 

9706 

3 

.0601 

4 

•  695 

5 

3769 

o 

0108 

4 

.978 

5 

3743 

8 

5335 

7 

0585 

[5 

0353] 

3 

.0620 

5 

.306 

5 

3752 

5. 

0883 

5 

.501 

5 

3677 

8 

.5286 

7 

0463 

5 

1307 

3 

0585 

5 

.500 

5 

3694 

8 

5309 

•7 

.0484 

5- 

H36 

3 

0593 

5 

.689 

5 

3668 

8 

5126 

tj 

0441 

5- 

1952 

[3 

0763] 

5 

.845 

5 

3630 

8 

5009 

•7 

0477 

$:• 

2516 

O 

.0880 

6 

.200 

5 

3688 

8 

4967 

5' 

2621 

6 

•550 

[5 

3971] 

8. 

5035 

7 

0452 

5- 

2934 

3 

1532 

6 

.844 

5 

.4290 

8 

4908 

7 

O426 

5- 

3506 

3' 

1779 

7 

.387 

5 

•5157 

[8- 

5447] 

[7 

0863] 

3 

2498 

7 

.859 

5 

.5766 

8.6058 

7- 

1340 

3' 

3201 

Table  VI  are  given  the  values  of  w/d  for  each  liquid  on  each 
tip.     From  this  all  those  things  mentioned  above  as  to  the 

1  In  this  connection  it  may  be  said  that  the  5.501  tip  is  the  one  used 
by  Morgan  and  Thomssen,  the  results  here  being  slightly  lower,  due  to 
slight  flaws,  presumably,  which  have  since  developed. 


19 

bulging  or  the  loss  of  control  are  made  clearer  than  they 
would  be  in  a  small  curve,  for  the  difference  there  would 
hardly  be  noticeable. 

It  will  be  noted  here  that  from  3.929  to  4.514  the  value  of 
w/d  for  carbon  tetrachloride  is  constant  and  then  increases 
continually  with  the  size  of  the  tip,  showing  the  effect  of 
lack  of  control,  and  later  the  combination  of  that  with  the 
pulling  away  of  the  drop  from  the  edge ;  while  for  all  the  other 
liquids,  on  the  contrary,  up  to  4.514  the  value  decreases  then 
remains  constant  for  a  greater  or  less  variation  in  diameter. 
The  loss  of  control  of  ether  is  first  observed  on  the  5.689  tip, 
while  benzene  is  lost  on  the  6.55,  and  pyridine  and  qivinoline 
on  the  7.387. 

TABLE  VII. — NORMAL  BENZENE  CONSTANTS. 

Diameter  /M\  § 

of  tip. 


Mm.  \d/  288.5  —  27.8  —  6 

3.048  347-51  I-3644 

3.929  431-77  1.6952 

4.000  439 .18  I-7243 

4.514  485-72  1.9078 

4.695  505-47  1.9846 

4.978  535-67  2.1032 

5.306  571-17  2.2425 

5-501  591-23  2.3213 

5.500  59I-3I  2.3216 

5.689  611.33  2.4002 

5.845  627.70  2.4645 

6.200  666.48  2.6168 

6.550  707.82  2.7791 

6.844  743-97  2.9210 

7-387  815.91  3-2034 

7-859  877.58  3-4456 

The  4.514  tip  is  the  only  one  which  gives  correct  results  for 
carbon  tetrachloride,  for  above  this  tip  the  results  are  too 
high,  due  to  lack  of  control;  while  below  it,  it  is  impossible 
to  use  benzene  as  the  standard  because  of  the  bulging  of  the 
drop.  The  carbon  tetrachloride  k  is  then  the  only  true  one 
for  small  tips,  and  hence  in  the  future  will  be  the  liquid  used 
for  the  standardization  of  small  tips  when  they  are  used  for 


20 

determining  the  drop  weights  of  liquids  similar  to  that  of 
carbon  tetra  chloride,  i.  e.,  liquids  with  a  very  high  density 
and  small  surface  tension.  The  value  of  tc  is  then  to  be  taken 
as  283.15°  as  found  on  the  4.514  tip,  and  the  normal  value 
of  the  constant  k  of  the  tip  calculated  from  it. 

In  Table  VII  are  the  kB  values  found  from    benzene   by 
use  of  the  formula 


=£B(288.5  —  27.8  —  6) 

Wherever  both  benzene  and  the  other  liquid  give  constant 

weisfht 

results  of  -          —  we  would  expect  to  find  a  constant  value 
diameter 

of  k  necessary  to  give  the  values  of  tc  as  found  from  the  work 
of  Morgan  and  Higgins  by  Morgan,1  on  substituting  the 
values  of  M  and  d  for  that  liquid  in 


These  tc  values  are  346.6°  for  pyridine,  521.3°  for  quinoline, 
195°  for  ether  and  283.2°  for  carbon  tetrachloride. 


TABLE  VIII.— 


M 

w    — 


tc  —  27.8—  6 
Diameter 
of  tip. 
mm.  Benzene.  Quinoline.         Pyridine.  Ether.  CCL*. 


4.514  1.9078  I.9Ol6o       I.9O46I        I.9O9I          1.9081 

4.695  1.9846  [2.0004] 

4.978  2.IO32  2.IOT36       2.10^54       2.1066        [2.I3II] 

5.307  2.2425  [2.2777] 

5.500  2.3216      2.32^35     2.3^230     2.3256      [2.3856] 

5.501  2.3213       2.3233       2.32^30       2.3254      [2.3801] 
5.689       2.4002       2.4037       2.4012      [2.4188] 

In  Table  VIII  are  given  those  k  values  for  the  tips  from 
4.514-5.501  inclusive,  between  which  we  should  expect  the 
liquids  to  be  concordant  in  result,  with  the  exception  of 

weicrht 

carbon  tetrachloride,  since  the  values  of  —. —        -  are  constant 

diameter 

1  J.  A.  C.  S.,  May,  1911. 


21 


on  them.  The  value  of  this  latter  on  the  4.695  tip  shows 
the  effect  of  the  lack  of  perfect  control  which  was  noted 
when  the  determination  was  made. 

Since,  as  has  been  shown  by  Morgan,  surface  tension  in 
dynes  can  be  found  from  drop  weight  in  milligrams  by  aid  of  the 
proportion 

f\-w\  :KB  :  &B, 

where  KB  is  the  value  found  from  Ramsay  and  Shields  very 
accurate  benzene  values,  calling  tc  =  288.5°,  *•  e->  2.1012; 
while  kB  is  the  similarly  determined  value  for  drop  weight 
on  the  tip  in  question  (see  Table  VIII). 

Table  IX  contains  the  values  of  surface  tension  in  dynes, 
calculated  from  drop  weight  in  milligrams  by  aid  of  the 
above  relation  for  the  tips  considered  in  Table  VIII. 

TABLE  IX. — SURFACE  TENSIONS. 


Diameter 

of  tip. 

*» 

Quinoline. 

Pyridine. 

Ether. 

CCU. 

4-5*4 

4-695 
4  •  978 

I  .  9078 
I  .  9846 
2.1032 

42-39 

42.44 

35-04 

35-io 

15.22 
I5-23 

24.71 

5  •  307 

2.2425 

5-501 
5-500 
5.689 

2.3213 
2.3216 
2  .  4OO2 

42.47 
42.47 
42.49 

35-09 
35-09 
35-o8 

I5-23 
I5-23 
[I5-32] 

Average,     42.45       35.08        15.23 


TABLE  X. — k  VALUES. 


Diameter 
of  tip. 

Mm. 

Benzene. 

Quinoline. 

Pyridine. 

Ether. 

ecu. 

3-048 

1.3644 

I-3897 

I  .3601 

1.3603 

1-3194 

3-929 

1.6952 

I  .7121 

I.697I 

1.6977 

1.6722 

4.000 

I-7243 

I.74H 

1.7264 

1.7272 

I  .  7007 

-5-689 

2  .  4002 

2.4037 

2.4012 

2.4188 

2.4930 

5-845 

2.4645 

2  .  4608 

2.4685 

2.4883 

2.5893 

6.200 

2.  6l68 

2.6088 

2.7524 

6.550 

2.7791 

2.7582 

2.7651 

2.8552 

2.9245 

6.844 

2.9210 

2.8777 

2.8881 

3  .  0046 

3.0888 

7.387 

3-3034 

3.1260 

3.1368 

3-3181 

7.859 

3-4456 

3-3495 

3.3601 

3.6065 

22 

Table  X  contains  the  k  values  and  Table  XI  the  7-  values 
calculated  similarly  for  the  other  tips,  which  from  their 

weight 
j: —  relations  should  not  be  perfectly  satisfactory. 

It  will  be  noted  here  that  the  results  are  exactly  what  has 
already  been  shown  by  the  simpler  w/d  ratios,  so  that  we 
need  not  discuss  them  further. 


TABLE  XI. — SURFACE  TENSIONS. 


Diameter, 
of  tip. 


Mm. 

Benzene. 

Quinoline. 

Pyridine. 

Ether. 

CC14. 

3 

.048 

26 

•73 

43 

.21 

34 

.96 

15 

.16 

23 

.89 

3 

929 

26 

•73 

42 

•85 

35 

.  10 

15 

.  22 

24 

•37 

4 

.000 

26 

•73 

42 

•85 

35 

.11 

15 

•23 

24 

•37 

5 

.689 

26 

•73 

42 

•49 

35 

.08 

15 

•32 

25 

.87 

5 

.845 

26 

•73 

42 

•37 

35 

.  12 

15 

•35 

26 

17 

6 

.200 

26. 

73 

42 

30 

26. 

20 

6 

•  550 

26 

73 

42 

.  ii 

34 

89 

15 

.62 

26. 

21 

6 

.844 

26. 

73 

4* 

80 

34 

67 

15 

.64 

26. 

34 

7 

.387 

26 

•73 

4i 

.40 

34 

34 

15 

•75 

7 

.859 

26 

73 

41 

25 

34 

20 

15 

.91 

For  benzene,  using  the  value  of  w/d  (see  Table  VI)  we 
find  the  following  relationships  (holding  for  tips  from  4.514 
to  5.501  inclusive), 


and 

w  =  1.710  X  7T  X  2  r 

where  w  is  given  in  milligrams  and  r  in  millimeters.  The 
relationship  existing  between  diameter,  drop  weight  and 
surface  tension  in  dynes  per  cm.  (found  from  the  above, 
knowing  further  that  w  —  constant  X  7*)  for  any  liquid  is 
then 

w  =  0.063972  X  (2  r)  x  r- 

Although  this  relationship  was  found  for  benzene  it  must 
hold  for  all  the  other  liquids  since  the  assumption  in  obtain- 
ing it  was  only  that  w  is  proportional  to  7-. 

In  Table  XII  are  given  the  values  of  7-  as  calculated  from 
the  above  equation. 


23 

XII. — SURFACE  TENSIONS. 


Diameter 
of  tip. 

Mm. 

Benzene. 

Quinoline. 

Pyridine.              CC14. 

Ether. 

4-5I4 

26.75 

42.42 

35.06             24.73 

I5-23 

4-695 

26.75 

4.978 

26.74 

42.46 

35-12 

I5-24 

5-306 

26.75 

5-500 

26.72 

42-45 

35-07 

15.22 

5-501 

26.71 

42.44 

35-06 

15.22 

5.689 

26.70 

42.45 

35-05 

[I5-3I] 

Av.,       26.73         42-44         35-07         24.73  15.23 

Conclusions. 

I.  The  drop  weights  of  benzene,  quinoline,  pyridine, 
ether  and  carbon  tetrachloride  have  been  determined  at  a 
constant  temperature  from  sixteen  different  .tips  varying 
in  size  from  3.048  to  7.859  mm.  in  diameter. 

II.  All  liquids  from  water,  forming  practically  the 
largest  drop  volume  to  carbon  tetrachloride,  practically  the 
smallest,  follow  Tate's  law  as  to  proportionality  with  surface 
tension  on  a  tip  of  4.514  mm.  diameter;  while,  excluding 
carbon  tetrachloride  and  a  few  similar  liquids  with  small 
surface  tensions  and  large  densities,  the  law  is  found  to  hold 
rigidly  on  tips  between  4.514  and  5.501  mm. 

III.  Smaller  tips  than  4.514  are  adapted  only  to  related 
liquids  when  the  lower  end  of  the  drop  bulges  in  the  same 
way,  or  those  which  like  carbon  tetrachloride  form  on  them 
normal  looking  drops  similar  to  those  of  other  liquids  on  the 
larger  tips. 

IV.  Tips  larger   than   5.501    will  also  hold  for   similar 
liquids  only,  for  here  it  is  simply  a  question  of  the  perfection 
in  the  control  of  the  drop. 

V.  All  these  things  can  be  observed  by  closely  watching 
the  drop;  and  a  liquid  can  be  said  to  be  satisfactory  or  not 
as  soon  as  its  drop  profile  on  the  tip  in  question  is  observed. 
This  is  also  shown  for  a  series  of  tips  by  the  values  of  the 

weight 

ratios  —. —     -  . 
diameter 


VI.  Surface  tensions  in  dynes  per  cm.  calculated  from 
drop  weight  in  milligrams  by  multiplication  with  the  ratio  of 
kr/kw  show  the  same  values  for  the  liquids  considered  when 
calculated  for  all  tips,  the  variation  being  considerably 
smaller  than  that  from  capillary  rise  by  the  same  observers 
with  different  tubes. 

VII.  It  is  found  that  drop  weight  in  milligrams,  diameter 
of  the  tip  in  millimeters  and  surface  tension  in  dynes  are 
related,  for  tips  from  4.514  to  5.501  by  the  following  equation 
w  =  0.063972  (2  r)  n  f 

VIII.  It  is  shown  clearly  why  such  a  law  cannot  hold  for 
all  liquids  on  smaller  or  larger  tips  than  these,  but  it  must  be 
recognized  that  even  on  tips  beyond  these,  in  either  direction, 
that  the  results,  in  terms  of  surface  tension,  agree  with  the 
others  fully  as  well  as  do  those  values  determined  by  aid  of 
capillary  rise  by  various  observers. 


BIOGRAPHY. 

Jessie  Yereance  Cann  was  born  May  17,  1883,  in  Newark, 
New  Jersey.  In  June  1901  she  graduated  from  the  Newark 
High  School,  and  was  awarded  a  four-year  scholarship  in  the 
Woman's  College  of  Baltimore  (Goucher  College).  She 
completed  her  college  course  in  three  years,  receiving  the 
degree  of  A.B.  in  June,  1904.  During  the  years  1904-1909 
she  taught  Science  in  the  Belleville  (N.  J.)  High  School. 
She  was  a  graduate  student  in  Physical  Chemistry  at  Colum- 
bia University  during  the  years  1909-1911,^3  well  as  during 
the  Summer  Sessions  of  1907,  1908,  1909  and  1910;  and  the 
holder  of  a  Curtis  Scholarship  1909-1910,  receiving  the  degree 
of  A.M.  in  June,  1910. 


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